$-2x^2+6x-3=0 \\ \\
a=-2 \\ b=6 \\ c=-3 \\ \Delta=b^2-4ac=6^2-4 \times (-2) \times (-3)=36-24=12$

The value of the discriminant is 12.
Since the discriminant is greater than zero, the equation has two real solutions.

4 0

3 years ago

Convert the exponential function to the form indicated. (Round all coefficients to four significant digits.) f(x) = 2.5 e^(-0.7

Jobisdone [24]

$f(x)=2.5e^{-0.7x}=2.5\left(e^{-0.7}\right)^x\\\\A=2.5\\\\b=e^{-0.7}$

5 0

3 years ago

Determine the equation of the circle with radius 99 and center (-1,-8)(−1,−8).

kumpel [21]

<h2>Equations of Circles</h2>

Generally, you'd see the equation of a circle organized in the following format:

$(x-h)^2+(y-k)^2=r^2$

$(h,k)$ is the center
$r$ is the radius

To determine the equation given the center and the radius:

Plug both pieces of information into the general equation
Simplify

<h2>Solving the Question</h2>

We're given:

Radius: 99
Center: (-1,-8)

Plug the radius and center into the equation as r and (h,k):

$(x-(-1))^2+(y-(-8))^2=99^2\\(x+1)^2+(y+8)^2=9801$

<h2>Answer</h2>

$(x+1)^2+(y+8)^2=9801$

7 0

2 years ago